Some problems are evaluated in terms of quality versus correct or incorrect. Such problems are known as optimization problems because the goal is the identification of the optimal value. Functions (sometimes called cost functions, objective functions, error functions, and so on.) achieve that goal by mapping n-dimensional real-valued items into one-dimensional real-valued items (some folks will prefer the termspaces over items' as it more closely aligns with the total search space we have talked about).

There are two types of function we will deal with. They are:

• Minimization: Looking for the solution with the smallest value
• Maximization: Looking for the solution with the largest value

It is not always the case that we can find the minimum or maximum, but sometimes must settle on a value that we deem sufficiently good enough for what we are trying to accomplish.